We show that the electronic coupling and magnetic moment of a silver nanoparticle dimer can be readily tuned by applying an electric field in the nonlinear dielectric-response regime. For a given interparticle separation, the electronic coupling becomes tunable as soon as the system crosses over from the linear to nonlinear regime. Remarkably, this transition takes place for modest strengths of the electric field. Further increase of the field strength may close the HOMO-LUMO gap of the dimer due to Stark shifts, accompanied by the emergence of a net magnetic moment from two nonmagnetic building blocks. These findings, obtained within density functional theory, exhibit the delicate coupling between the electronic and magnetic degrees of freedom and point to new approaches to gain multifunctionality of nanoparticle aggregates.